Parametrix techniques and martingale problems for some degenerate Kolmogorov equations
By Stéphane Menozzi. 2010
64 citations recorded by the source corpus.
We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins [BP09] to prove uniqueness of the martingale problem in the framework of non- degenerate elliptic operators and the Mc Kean and Singer [MS67] parametrix approach to the density expansion that has previously been extended to the degenerate setting that we consider (see Delarue and Menozzi [DM10]).
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb97a527ba2b62f7b5648fd6bec6168dca9be460
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise (2015, background): “proximate harmonic functions for the operators ∂t −L,∂t +L; see Section 4.3. We feel that the idea behind this argument is close to the one developed in the diffusion setting in [BP09] and extended in [M11], [HM14], though the particular form of the argument is different. We mention also that using pr”